Math / Geometry

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Triangle HIJ is dilated by a scale factor of $\frac{2}{3}$ to form triangle H'I'J'. What is the measure of side I'J'? Answer Attempt 1 out of 3

Studdy Solution

STEP 1

1. Triangle HIJ is similar to triangle H'I'J' due to dilation.
2. The scale factor of the dilation is $\frac{2}{3}$ .
3. The side length $IJ$ of triangle HIJ is $42$ .

STEP 2

1. Understand the relationship between the original and dilated triangles.
2. Apply the scale factor to the side length of the original triangle.
3. Calculate the length of side $I'J'$ .

STEP 3

Understand the relationship between the original and dilated triangles:
Since triangle H'I'J' is a dilation of triangle HIJ, all corresponding sides of triangle H'I'J' are proportional to the sides of triangle HIJ by the scale factor $\frac{2}{3}$ .

STEP 4

Apply the scale factor to the side length of the original triangle:
The side $IJ$ of triangle HIJ is $42$ . To find the corresponding side $I'J'$ in triangle H'I'J', multiply $IJ$ by the scale factor:
$I'J' = IJ \times \frac{2}{3}$

STEP 5

Calculate the length of side $I'J'$ :
$I'J' = 42 \times \frac{2}{3}$ $I'J' = 28$
The measure of side $I'J'$ is:
$\boxed{28}$

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Questionvs Similarity
Question Show Examples
Triangle HIJ is dilated by a scale factor of $\frac{2}{3}$ to form triangle H'I'J'. What is the measure of side I'J'? Answer Attempt 1 out of 3

Studdy Solution

STEP 1

1. Triangle HIJ is similar to triangle H'I'J' due to dilation.
2. The scale factor of the dilation is $\frac{2}{3}$ .
3. The side length $IJ$ of triangle HIJ is $42$ .

STEP 2

1. Understand the relationship between the original and dilated triangles.
2. Apply the scale factor to the side length of the original triangle.
3. Calculate the length of side $I'J'$ .

STEP 3

Understand the relationship between the original and dilated triangles:
Since triangle H'I'J' is a dilation of triangle HIJ, all corresponding sides of triangle H'I'J' are proportional to the sides of triangle HIJ by the scale factor $\frac{2}{3}$ .

STEP 4

Apply the scale factor to the side length of the original triangle:
The side $IJ$ of triangle HIJ is $42$ . To find the corresponding side $I'J'$ in triangle H'I'J', multiply $IJ$ by the scale factor:
$I'J' = IJ \times \frac{2}{3}$

STEP 5

Calculate the length of side $I'J'$ :
$I'J' = 42 \times \frac{2}{3}$ $I'J' = 28$
The measure of side $I'J'$ is:
$\boxed{28}$

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Questionvs SimilarityQuestion Show ExamplesTriangle HIJ is dilated by a scale factor of 23\frac{2}{3}32​ to form triangle H'I'J'. What is the measure of side I'J'? Answer Attempt 1 out of 3

Studdy Solution

STEP 1

1. Triangle HIJ is similar to triangle H'I'J' due to dilation.2. The scale factor of the dilation is 23\frac{2}{3}32​.3. The side length IJIJIJ of triangle HIJ is 424242.

STEP 2

1. Understand the relationship between the original and dilated triangles.2. Apply the scale factor to the side length of the original triangle.3. Calculate the length of side I′J′I'J'I′J′.

STEP 3

Understand the relationship between the original and dilated triangles:Since triangle H'I'J' is a dilation of triangle HIJ, all corresponding sides of triangle H'I'J' are proportional to the sides of triangle HIJ by the scale factor 23\frac{2}{3}32​.

STEP 4

Apply the scale factor to the side length of the original triangle:The side IJIJIJ of triangle HIJ is 424242. To find the corresponding side I′J′I'J'I′J′ in triangle H'I'J', multiply IJIJIJ by the scale factor:I′J′=IJ×23 I'J' = IJ \times \frac{2}{3} I′J′=IJ×32​

STEP 5

Calculate the length of side I′J′I'J'I′J′:I′J′=42×23 I'J' = 42 \times \frac{2}{3} I′J′=42×32​ I′J′=28 I'J' = 28 I′J′=28 The measure of side I′J′I'J'I′J′ is:28 \boxed{28} 28​

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Questionvs Similarity
Question Show Examples
Triangle HIJ is dilated by a scale factor of $\frac{2}{3}$ to form triangle H'I'J'. What is the measure of side I'J'? Answer Attempt 1 out of 3

1. Triangle HIJ is similar to triangle H'I'J' due to dilation.
2. The scale factor of the dilation is $\frac{2}{3}$ .
3. The side length $IJ$ of triangle HIJ is $42$ .

1. Understand the relationship between the original and dilated triangles.
2. Apply the scale factor to the side length of the original triangle.
3. Calculate the length of side $I'J'$ .

Understand the relationship between the original and dilated triangles:
Since triangle H'I'J' is a dilation of triangle HIJ, all corresponding sides of triangle H'I'J' are proportional to the sides of triangle HIJ by the scale factor $\frac{2}{3}$ .

Apply the scale factor to the side length of the original triangle:
The side $IJ$ of triangle HIJ is $42$ . To find the corresponding side $I'J'$ in triangle H'I'J', multiply $IJ$ by the scale factor:
$I'J' = IJ \times \frac{2}{3}$

Calculate the length of side $I'J'$ :
$I'J' = 42 \times \frac{2}{3}$ $I'J' = 28$
The measure of side $I'J'$ is:
$\boxed{28}$